Closing the SU(3){sub L}xU(1){sub X} symmetry at the electroweak scale

We show that some models with SU(3){sub C}xSU(3){sub L}xU(1){sub X} gauge symmetry can be realized at the electroweak scale and that this is a consequence of an approximate global SU(2){sub L+R} symmetry. This symmetry implies a condition among the vacuum expectation value of one of the neutral Higgs scalars, the U(1){sub X}'s coupling constant, g{sub X}, the sine of the weak mixing angle sin{theta}{sub W}, and the mass of the W boson, M{sub W}. In the limit in which this symmetry is valid it avoids the tree level mixing of the Z boson of the standard model with the extra Z{sup '} boson. We have verified that the oblique T parameter is within the allowed range indicating that the radiative corrections that induce such a mixing at the 1-loop level are small. We also show that a SU(3){sub L+R} custodial symmetry implies that in some of the models we have to include sterile (singlets of the 3-3-1 symmetry) right-handed neutrinos with Majorana masses, since the seesaw mechanism is mandatory to obtain light active neutrinos. Moreover, the approximate SU(2){sub L+R} subset of SU(3){sub L+R} symmetry implies that the extra nonstandard particles of these 3-3-1 models can be considerably lighter than itmore » had been thought before so that new physics can be really just around the corner.« less